Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 354: 57

Answer

$\dfrac{-2x-1}{x^3-3x^2}$

Work Step by Step

The expressions are not similar since they have different denominators. To make the expressions similar, find the LCD (least common denominator) first. Factor each denominator to have: $\\x^2-3x=x(x-3) \\x^3-3x^2=x^2(x-3)$ Thus, the LCD is $x^2(x-3)=^3-3x^2$. Make the expressions similar using their LCD to have: $\\=\dfrac{-2(x)}{(x^2-3x)(x)} -\dfrac{1}{x^3-3x} \\=\dfrac{-2x}{x^3-3x^2}-\dfrac{1}{x^3-3x^2} \\=\dfrac{-2x-1}{x^3-3x^2}$
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